Abstract

We optimize the threshold gain for cylindrical composite (semiconductor–dielectric–metal) waveguides (WGs) with various metal claddings. We show that the optimal dielectric width is invariant with respect to the imaginary part of the permittivity of the metal, εM′′, and weakly dependent on the real part, εM′. To explain this behavior, we compare optimal geometries of WGs with different semiconductor permittivities, εG′. Results from these comparisons indicate that the optimal effective index parallels the optimal threshold gain in its relation to εM. We use our results to heuristically propose an analytical expression for the optimal threshold gain that approximates the numerical solution to within a factor of two over the range of explored εG′. Finally, we use data from our optimizations to obtain approximate analytical expressions for the optimal dielectric width and threshold gain as functions of the total WG radius.

Figures (7)

Re(sqrt(εR)) and |E| of the TE01 mode as functions of radial distance in an optimized composite WG (CWG) at λ0=1.55μm. The permittivities are εG=11.56+j8.65e−4, εD=2.16, and εM=−130−j3.0, respectively.

neff′ as function of Rcore for two values of εG′, with εM parameterized. Blue rectangles and red circles indicate (Rcore,neff)=(Rcore,opt,neff,opt) for InGaAsP and GaS CWGs, respectively. εD, λ0, and Rtotal are fixed at 2.16, 1.55, and 0.45 μm, respectively.

Error in Eq. (2), with εGth′′ and neff substituted for εGth,opt′′ and neff,opt, relative to the numerical solution of Eq. (1) as a function of Rcore with εG′ parameterized. εD, εM, λ0, and Rtotal are fixed at 2.16, −130−j3.0, 1.55, and 0.45 μm, respectively.

ΔD,opt and log10(εGth,opt′′) as functions of Rtotal. The red (on red line from lower left to upper right) and blue (on blue line from upper left to lower right) solid triangles correspond to numerical solutions of Eq. (1), whereas the red and blue lines correspond to linear approximations for ΔD,opt and log10(εGth,opt′′), respectively. εM, εD, εG′, and λ0 are fixed at −130−j3.0, 2.16, 11.56, and 1.55 μm, respectively.